Abstract

The relation between a three-dimensional (3D) object and its diffracted wavefront in the 3D Fourier space is discussed at first and then a rigorous diffraction formula onto cylindrical surfaces is derived. The azimuthal direction and the spatial frequency direction corresponding to height can be expressed with a one-dimensional (1D) convolution integral and a 1D inverse Fourier transform in the 3D Fourier space, respectively, and fast Fourier transforms are available for fast calculation. A numerical simulation of a diffracted wavefront on cylindrical surfaces is presented. An alternative optical experiment equivalent of the optical reconstruction from cylindrical holograms is also demonstrated.

© 2013 Optical Society of America

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References

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2013

2012

2010

2008

2005

2002

1993

N. Hashimoto and S. Morokawa, J. Electron. Imaging 2, 93 (1993).
[CrossRef]

1982

1976

1967

Barada, D.

Fernandes, J. C. A.

Fujii, T.

Geong, T. H.

Hashimoto, N.

N. Hashimoto and S. Morokawa, J. Electron. Imaging 2, 93 (1993).
[CrossRef]

Itoh, M.

Jackin, B. J.

Kashiwagi, A.

A. Kashiwagi and Y. Sakamoto, Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2007), paper DWB7.

Lohmann, A. W.

Mishina, T.

Morokawa, S.

N. Hashimoto and S. Morokawa, J. Electron. Imaging 2, 93 (1993).
[CrossRef]

Okano, F.

Okui, M.

Paris, D. P.

Sakamoto, Y.

A. Kashiwagi and Y. Sakamoto, Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2007), paper DWB7.

Sando, Y.

Soares, O. D. D.

Yamaguchi, T.

Yatagai, T.

Yoshikawa, H.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the virtual optical system for observation of diffracted wavefronts.

Fig. 2.
Fig. 2.

Coordinate system (θ,v) for representing the spectrum on the spherical surface.

Fig. 3.
Fig. 3.

Schematic of the virtual optical system for calculation of wavefronts on the cylindrical surface: (a) perspective view and (b) top view.

Fig. 4.
Fig. 4.

Simulation results. The horizontal and vertical axes represent the azimuth angle ϕ and the height y, respectively. (a), (b), and (c) are calculated under the conditions of R=0.8D, 1.0D, and 1.2D, respectively. (d) is calculated without hidden surface removal for R=1.0D.

Fig. 5.
Fig. 5.

Schematics of (a) a cutout of a segmented CGH and the radial projection onto the tangent plane and (b) the optical reconstruction system from the segmented CGH.

Fig. 6.
Fig. 6.

Segment of the cylindrical CGH.

Fig. 7.
Fig. 7.

Optically reconstructed images captured from the different segmented CGHs corresponding to ϕ= (a) 0°, (b) 45°, (c) 135°, and (d) 90°, respectively.

Equations (7)

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f0(x0,y)=i4πO(u,v,1/λ2u2v2)1/λ2u2v2×exp(i2πR1/λ2u2v2)×exp[i2π(ux0+vy)]dudv.
u=1λ2v2sinθv=v,
f0(0,y)=i4ππ/2π/2Os(θ,v)exp(i2πRcosθ1/λ2v2)×exp(i2πvy)dθdv.
f0(0,y)=i4πππOs(θ,v)exp(i2πRcosθ1/λ2v2)×rect[θπ]exp(i2πvy)dθdv.
fc(ϕ,y)=i4πππOs(θ,v)×exp[i2πRcos(θϕ)1/λ2v2]×rect[θϕπ]exp(i2πvy)dθdv.
h(θ,v)=exp(i2πRcosθ1/λ2v2)rect[θπ].
fc(ϕ,y)=i4π[Os(ϕ,v)ϕ*h(ϕ,v)]exp(i2πvy)dv,

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